10. a vertical electric field of magnitude $2.00 \times 10^4\text{ n/c}$ exists above the earths surface on a day when a thunderstorm is brewing. a car with a rectangular size of $6.00\text{ m}$ by $3.00\text{ m}$ is traveling along a dry gravel roadway sloping downward at $10.0^\circ$. determine the electric flux through the bottom of the car.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Electrostatics" ], "new_concepts": [ "Electric Flux", "Flux Through Inclined Surface" ], "current_concepts": [ "Electrostatics", "Electric Flux", "Flux Through Inclined Surface" ] } ## Identify given parameters and formula $$ \begin{aligned} E &= 2.00 \times 10^4 \text{ N/C} \quad (\text{vertical field}) \ A &= 6.00 \text{ m} \times 3.00 \text{ m} = 18.0 \text{ m}^2 \ \theta &= 10.0^\circ \quad (\text{angle of the slope relative to the horizontal}) \ \Phi_E &= E A \cos\theta \end{aligned} $$ ## Calculate the electric flux $$ \begin{aligned} \Phi_E &= (2.00 \times 10^4 \text{ N/C}) \times (18.0 \text{ m}^2) \times \cos(10.0^\circ) \ \Phi_E &= 3.60 \times 10^5 \times 0.9848077 \ \Phi_E &\approx 3.55 \times 10^5 \text{ N}\cdot\text{m}^2/\text{C} \end{aligned} $$ $3.55 \times 10^5 \text{ N}\cdot\text{m}^2/\text{C}$ { "subject": "Natural Science", "question_type": "Free Response", "knowledge_point": [ "Natural Science", "Physics", "Electric Flux" ] }

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Identify given parameters and formula

Calculate the electric flux

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